Question

A resistor ladder digital-to-analog converter (DAC) receives a digital input that results in the circuit having the state as shown in the figure. For this digital input, the Thevenin voltage, \( V_{th} \), and Thevenin resistance, \( R_{th} \), as seen at the output node are _________

• A. ( V_{th} = 0.5 \, \text{V}, R_{th} = 1 \, \text{k}\Omega \)
• B. ( V_{th} = 0.5 \, \text{V}, R_{th} = 2 \, \text{k}\Omega \)
• C. ( V_{th} = 1 \, \text{V}, R_{th} = 1 \, \text{k}\Omega \)
• D. ( V_{th} = 1 \, \text{V}, R_{th} = 2 \, \text{k}\Omega \)

Hint:

In resistor ladder DACs, the Thevenin voltage depends on the digital input, and the Thevenin resistance is determined by the parallel combination of resistors in the ladder.

Answer 1

The Correct Option is C

Step 1: Analyzing the Resistor Ladder DAC.
In a resistor ladder DAC, the Thevenin voltage \( V_{th} \) is the voltage across the resistors in the ladder, which depends on the digital input. The Thevenin resistance \( R_{th} \) is the equivalent resistance seen at the output node, which is determined by the resistors in the ladder. Step 2: Analyzing the circuit configuration.
From the given circuit, there are resistors arranged in a ladder configuration. The Thevenin voltage can be calculated by determining the voltage divider formed by the resistors. Based on the configuration, the Thevenin voltage is \( 1 \, \text{V} \), and the Thevenin resistance is the equivalent resistance of the two 1 kΩ resistors in parallel, which results in \( 1 \, \text{k}\Omega \). Step 3: Conclusion.
Thus, the Thevenin voltage \( V_{th} = 1 \, \text{V} \) and Thevenin resistance \( R_{th} = 1 \, \text{k}\Omega \), making the correct answer (C).